In the arrangement P N 3 W 9 Q 1 8 L K 4 6 B 7, all the numbers are first placed in descending order, followed by all the letters placed in alphabetical order. In this new arrangement, which element is fourth to the left of the 11th element from the left end?

Introduction / Context:
This question tests your ability to rearrange a mixed sequence of numbers and letters according to specific rules and then apply positional counting from the left. Such sequence based problems are standard in reasoning sections of competitive exams. They require attention to the order in which items are rearranged and the ability to track positions after the rearrangement is complete. Here, you must move all numbers to the front in descending order, then place letters in alphabetical order, and finally locate a particular element relative to another element’s position.

Given Data / Assumptions:
1) Original sequence: P N 3 W 9 Q 1 8 L K 4 6 B 7.2) All numbers are to be rearranged in descending order first.3) All letters are then to be arranged in alphabetical order after the numbers.4) We must identify the element that is fourth to the left of the 11th element from the left end in the new sequence.

Concept / Approach:
The solution involves two main steps. First, separate numbers and letters, order them as instructed and write the new combined sequence. Second, use positional counting rules to locate the 11th element from the left and then move four positions to the left to find the required element. When dealing with positions like “kth from the left” and “mth to the left of that”, it is safer to mark index numbers underneath the sequence to avoid off by one errors.

Step-by-Step Solution:
1) Identify all numbers in the original sequence: 3, 9, 1, 8, 4, 6 and 7.2) Arrange these numbers in descending order: 9, 8, 7, 6, 4, 3, 1.3) Identify all letters: P, N, W, Q, L, K and B.4) Arrange letters in alphabetical order: B, K, L, N, P, Q, W.5) Combine the ordered numbers followed by the ordered letters to get the new sequence: 9, 8, 7, 6, 4, 3, 1, B, K, L, N, P, Q, W.6) Number the positions from the left: 1 9, 2 8, 3 7, 4 6, 5 4, 6 3, 7 1, 8 B, 9 K, 10 L, 11 N, 12 P, 13 Q, 14 W.7) The 11th element from the left is N. Fourth to the left of N means moving four positions leftward: from position 11 to 10, then 9, then 8, then 7. Position 7 holds the number 1.

Verification / Alternative check:
You can also calculate the target position numerically. If the 11th element is at position 11 and you need the element four places to its left, you compute 11 − 4 which gives position 7. Confirming the content of position 7 in the new sequence still yields 1. Cross checking by recounting from both ends ensures that no misalignment occurred during rearrangement. Because numbers and letters are grouped and ordered correctly and position 7 is clearly identified as 1, this verification supports the correctness of the answer.

Why Other Options Are Wrong:
K is at position 9, not position 7.3 is at position 6 and is therefore one place to the left of the required position.B is at position 8, which is one place to the right of the required position.None of these is incorrect because 1 appears explicitly at the correct position in the new sequence.

Common Pitfalls:
Some candidates forget to rearrange numbers and letters separately and instead sort the entire sequence purely alphabetically or numerically. Others miscalculate the descending order of numbers or the alphabetical order of letters. Off by one errors when counting “fourth to the left” are also very common, especially if you try to count mentally without writing positions. To avoid these mistakes, always separate and sort elements clearly, then label positions, and finally perform relative position calculations step by step.

Final Answer:
In the new arrangement, the element fourth to the left of the 11th element from the left is 1.